Is the OP saying that the line as is in the MyModule.pm code is incorrect, because the "special" nature of DEFAULT overrides it with something else?

Yes. Exporter.pm wants :DEFAULT to match @EXPORT so the module is incorrect in trying to define its own meaning for :DEFAULT. Based on what you've quoted, it appears that Exporter.pm forces this issue, but the more important point is that you shouldn't set $EXPORT_TAGS{DEFAULT} yourself.